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Bug 21094 reports 3ulp errors of cosf and tanf for certain arguments near pi/2 arising from the use of an insufficiently accurate range reduction. (To be clear, this is a quality-of-implementation issue relating to the apparent intent of those particular cosf and tanf implementations; 3ulp is within the general glibc accuracy goals, so not inherently a bug.) This patch fixes that error by making a wider range of cases use the existing more accurate range reduction for arguments close to pi/2. The wider range of values is still narrow enough for the "z -= pio2_2;" in the more accurate case to be exact, as the code expects. Tested for x86_64, x86 and mips64; no ulps updates needed (but at least on mips64, the larger ulps were seen if the tests were added without the substantive fix). [BZ #21094] * sysdeps/ieee754/flt-32/e_rem_pio2f.c (__ieee754_rem_pio2f): Use 24+24+24-bit pi for wider range of values around pi/2. * math/auto-libm-test-in: Add more tests of cos and tan. * math/auto-libm-test-out-cos: Regenerated. * math/auto-libm-test-out-tan: Likewise.
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